{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ReinforcementLearningAnIntroduction\n",
    "using StatsBase, Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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       "  475.559,1390.6 476.597,1390.92 477.634,1391.05 478.672,1391.15 479.71,1391.38 480.747,1391.62 481.785,1391.87 482.823,1391.81 483.861,1392.24 484.898,1392.37 \n",
       "  485.936,1392.47 486.974,1392.5 488.011,1392.98 489.049,1393.1 490.087,1393.21 491.125,1393.35 492.162,1393.62 493.2,1393.79 494.238,1394.18 495.275,1394.53 \n",
       "  496.313,1395.11 497.351,1395.06 498.389,1395.14 499.426,1395.3 500.464,1395.54 501.502,1395.59 502.539,1395.62 503.577,1395.61 504.615,1395.66 505.653,1395.85 \n",
       "  506.69,1395.66 507.728,1396.05 508.766,1396.61 509.803,1396.74 510.841,1396.8 511.879,1397.26 512.917,1397.7 513.954,1397.48 514.992,1397.51 516.03,1397.89 \n",
       "  517.067,1398 518.105,1398.16 519.143,1398.3 520.181,1398.5 521.218,1398.94 522.256,1399.12 523.294,1399.15 524.331,1399.25 525.369,1399.57 526.407,1399.5 \n",
       "  527.445,1399.92 528.482,1399.88 529.52,1399.66 530.558,1399.4 531.595,1399.46 532.633,1399.8 533.671,1400.2 534.709,1400.52 535.746,1400.76 536.784,1400.7 \n",
       "  537.822,1400.72 538.859,1400.84 539.897,1400.84 540.935,1401.14 541.973,1401.1 543.01,1401.15 544.048,1401.28 545.086,1401.47 546.123,1401.73 547.161,1401.66 \n",
       "  548.199,1401.7 549.237,1401.92 550.274,1402.08 551.312,1402.12 552.35,1402.33 553.388,1402.61 554.425,1402.54 555.463,1402.6 556.501,1402.77 557.538,1403.07 \n",
       "  558.576,1403.2 559.614,1403.38 560.652,1403.35 561.689,1403.62 562.727,1403.75 563.765,1403.76 564.802,1403.76 565.84,1403.92 566.878,1403.71 567.916,1403.99 \n",
       "  568.953,1404 569.991,1404.18 571.029,1404.52 572.066,1404.76 573.104,1405.37 574.142,1405.46 575.18,1405.34 576.217,1405.25 577.255,1405.3 578.293,1405.44 \n",
       "  579.33,1405.64 580.368,1405.78 581.406,1406.01 582.444,1405.94 583.481,1405.93 584.519,1406.1 585.557,1405.95 586.594,1406.25 587.632,1406.22 588.67,1406.27 \n",
       "  589.708,1406.38 590.745,1406.42 591.783,1406.74 592.821,1406.91 593.858,1406.87 594.896,1406.93 595.934,1407.04 596.972,1406.85 598.009,1406.68 599.047,1406.78 \n",
       "  600.085,1406.8 601.122,1406.9 602.16,1406.99 603.198,1407.31 604.236,1407.48 605.273,1407.64 606.311,1407.63 607.349,1407.79 608.386,1407.66 609.424,1407.84 \n",
       "  610.462,1407.84 611.5,1407.82 612.537,1407.85 613.575,1408.09 614.613,1408.27 615.65,1408.09 616.688,1408.39 617.726,1408.59 618.764,1408.86 619.801,1409 \n",
       "  620.839,1408.97 621.877,1408.89 622.914,1408.82 623.952,1408.87 624.99,1408.7 626.028,1408.67 627.065,1408.83 628.103,1408.9 629.141,1409.3 630.178,1409.54 \n",
       "  631.216,1409.69 632.254,1409.75 633.292,1409.71 634.329,1409.92 635.367,1409.85 636.405,1409.96 637.442,1410.06 638.48,1410.26 639.518,1410.28 640.556,1410.35 \n",
       "  641.593,1410.19 642.631,1410.21 643.669,1410.3 644.707,1410.5 645.744,1410.59 646.782,1410.52 647.82,1410.67 648.857,1410.82 649.895,1410.86 650.933,1411.06 \n",
       "  651.971,1411.18 653.008,1411.29 654.046,1411.44 655.084,1411.67 656.121,1411.78 657.159,1411.84 658.197,1411.91 659.235,1412.14 660.272,1412.34 661.31,1412.28 \n",
       "  662.348,1412.28 663.385,1412.26 664.423,1412.36 665.461,1412.38 666.499,1412.41 667.536,1412.49 668.574,1412.46 669.612,1412.5 670.649,1412.6 671.687,1412.67 \n",
       "  672.725,1412.78 673.763,1412.79 674.8,1412.83 675.838,1412.99 676.876,1413.11 677.913,1413.18 678.951,1413 679.989,1413.07 681.027,1413.13 682.064,1413.09 \n",
       "  683.102,1413.08 684.14,1412.98 685.177,1413.09 686.215,1413.29 687.253,1413.14 688.291,1413.22 689.328,1413.44 690.366,1413.35 691.404,1413.28 692.441,1413.4 \n",
       "  693.479,1413.35 694.517,1413.49 695.555,1413.51 696.592,1413.98 697.63,1414.11 698.668,1414.28 699.705,1414.2 700.743,1414.26 701.781,1414.56 702.819,1414.63 \n",
       "  703.856,1414.73 704.894,1414.78 705.932,1414.98 706.969,1414.8 708.007,1414.88 709.045,1415.09 710.083,1415.05 711.12,1415 712.158,1415.25 713.196,1415.29 \n",
       "  714.233,1415.72 715.271,1415.77 716.309,1415.8 717.347,1415.88 718.384,1415.92 719.422,1416.09 720.46,1416.26 721.497,1416.55 722.535,1416.54 723.573,1416.61 \n",
       "  724.611,1416.68 725.648,1416.71 726.686,1416.63 727.724,1416.64 728.762,1416.71 729.799,1416.64 730.837,1416.55 731.875,1416.52 732.912,1416.72 733.95,1416.82 \n",
       "  734.988,1417.04 736.026,1417.03 737.063,1416.94 738.101,1417.07 739.139,1417.16 740.176,1417.18 741.214,1417.36 742.252,1417.48 743.29,1417.69 744.327,1417.73 \n",
       "  745.365,1417.75 746.403,1417.7 747.44,1417.57 748.478,1417.69 749.516,1417.73 750.554,1417.68 751.591,1417.77 752.629,1417.7 753.667,1417.69 754.704,1417.59 \n",
       "  755.742,1417.51 756.78,1417.61 757.818,1417.69 758.855,1417.81 759.893,1417.78 760.931,1417.8 761.968,1417.74 763.006,1417.74 764.044,1417.86 765.082,1417.95 \n",
       "  766.119,1418.05 767.157,1417.96 768.195,1417.94 769.232,1418.15 770.27,1418.08 771.308,1418.23 772.346,1418.41 773.383,1418.67 774.421,1418.73 775.459,1418.68 \n",
       "  776.496,1418.8 777.534,1419.01 778.572,1419.03 779.61,1419.12 780.647,1419.36 781.685,1419.5 782.723,1419.62 783.76,1419.52 784.798,1419.51 785.836,1419.49 \n",
       "  786.874,1419.57 787.911,1419.7 788.949,1419.66 789.987,1419.65 791.024,1419.85 792.062,1419.86 793.1,1419.97 794.138,1419.91 795.175,1419.95 796.213,1419.92 \n",
       "  797.251,1419.96 798.288,1420.09 799.326,1420.08 800.364,1420.11 801.402,1420.14 802.439,1420.03 803.477,1419.9 804.515,1419.95 805.552,1419.8 806.59,1419.89 \n",
       "  807.628,1419.95 808.666,1420.02 809.703,1419.99 810.741,1419.93 811.779,1419.92 812.817,1419.93 813.854,1420.05 814.892,1420.15 815.93,1420.34 816.967,1420.35 \n",
       "  818.005,1420.34 819.043,1420.46 820.081,1420.49 821.118,1420.69 822.156,1420.82 823.194,1420.87 824.231,1420.9 825.269,1420.96 826.307,1421.01 827.345,1421.06 \n",
       "  828.382,1421.19 829.42,1421.17 830.458,1421.26 831.495,1421.36 832.533,1421.39 833.571,1421.38 834.609,1421.43 835.646,1421.32 836.684,1421.35 837.722,1421.32 \n",
       "  838.759,1421.53 839.797,1421.66 840.835,1421.66 841.873,1421.78 842.91,1421.81 843.948,1421.93 844.986,1422 846.023,1421.83 847.061,1421.76 848.099,1421.92 \n",
       "  849.137,1422.04 850.174,1421.99 851.212,1422.04 852.25,1422.08 853.287,1422.03 854.325,1422.05 855.363,1422.09 856.401,1422.22 857.438,1422.16 858.476,1422.06 \n",
       "  859.514,1422.14 860.551,1422.22 861.589,1422.27 862.627,1422.37 863.665,1422.45 864.702,1422.51 865.74,1422.65 866.778,1422.68 867.815,1422.71 868.853,1422.79 \n",
       "  869.891,1422.87 870.929,1422.91 871.966,1422.89 873.004,1423.02 874.042,1422.95 875.079,1422.91 876.117,1422.98 877.155,1422.87 878.193,1423.09 879.23,1422.97 \n",
       "  880.268,1423.01 881.306,1423.04 882.343,1423.25 883.381,1423.32 884.419,1423.36 885.457,1423.53 886.494,1423.42 887.532,1423.64 888.57,1423.56 889.607,1423.48 \n",
       "  890.645,1423.52 891.683,1423.62 892.721,1423.59 893.758,1423.82 894.796,1423.93 895.834,1423.94 896.871,1423.99 897.909,1424.07 898.947,1424.08 899.985,1424.03 \n",
       "  901.022,1423.96 902.06,1423.99 903.098,1423.94 904.136,1424.05 905.173,1424.11 906.211,1424.14 907.249,1424.2 908.286,1424.4 909.324,1424.48 910.362,1424.58 \n",
       "  911.4,1424.51 912.437,1424.47 913.475,1424.55 914.513,1424.7 915.55,1424.9 916.588,1424.86 917.626,1424.93 918.664,1424.85 919.701,1424.78 920.739,1424.83 \n",
       "  921.777,1424.82 922.814,1424.9 923.852,1425.12 924.89,1425.18 925.928,1425.19 926.965,1425.1 928.003,1425.1 929.041,1425.02 930.078,1425 931.116,1425.11 \n",
       "  932.154,1425.19 933.192,1425.25 934.229,1425.42 935.267,1425.55 936.305,1425.49 937.342,1425.46 938.38,1425.42 939.418,1425.52 940.456,1425.57 941.493,1425.6 \n",
       "  942.531,1425.53 943.569,1425.63 944.606,1425.7 945.644,1425.75 946.682,1425.66 947.72,1425.71 948.757,1425.8 949.795,1425.77 950.833,1425.84 951.87,1425.99 \n",
       "  952.908,1426.17 953.946,1426.18 954.984,1426.09 956.021,1426.11 957.059,1426.09 958.097,1426.1 959.134,1426.15 960.172,1426.12 961.21,1426.07 962.248,1426.21 \n",
       "  963.285,1426.3 964.323,1426.28 965.361,1426.25 966.398,1426.29 967.436,1426.39 968.474,1426.37 969.512,1426.54 970.549,1426.48 971.587,1426.56 972.625,1426.53 \n",
       "  973.662,1426.6 974.7,1426.61 975.738,1426.67 976.776,1426.76 977.813,1426.72 978.851,1426.69 979.889,1426.83 980.926,1426.85 981.964,1427.02 983.002,1426.94 \n",
       "  984.04,1427.04 985.077,1426.96 986.115,1427.03 987.153,1426.95 988.191,1427.04 989.228,1427.13 990.266,1427.11 991.304,1427.13 992.341,1427.07 993.379,1427.11 \n",
       "  994.417,1427.1 995.455,1427.17 996.492,1427.1 997.53,1427.05 998.568,1426.92 999.605,1427.04 1000.64,1426.93 1001.68,1427.07 1002.72,1427.12 1003.76,1427.24 \n",
       "  1004.79,1427.18 1005.83,1427.26 1006.87,1427.22 1007.91,1427.23 1008.94,1427.28 1009.98,1427.22 1011.02,1427.24 1012.06,1427.25 1013.1,1427.37 1014.13,1427.36 \n",
       "  1015.17,1427.3 1016.21,1427.33 1017.25,1427.5 1018.28,1427.63 1019.32,1427.8 1020.36,1427.91 1021.4,1427.94 1022.44,1428.01 1023.47,1428.05 1024.51,1428.02 \n",
       "  1025.55,1427.93 1026.59,1427.93 1027.62,1428.13 1028.66,1428.27 1029.7,1428.4 1030.74,1428.55 1031.77,1428.64 1032.81,1428.75 1033.85,1428.73 1034.89,1428.68 \n",
       "  1035.93,1428.75 1036.96,1428.78 1038,1428.81 1039.04,1428.94 1040.08,1429.02 1041.11,1429.15 1042.15,1429.28 1043.19,1429.29 1044.23,1429.27 1045.26,1429.2 \n",
       "  1046.3,1429.15 1047.34,1429.1 1048.38,1429.24 1049.42,1429.25 1050.45,1429.38 1051.49,1429.44 1052.53,1429.48 1053.57,1429.56 1054.6,1429.67 1055.64,1429.87 \n",
       "  1056.68,1429.88 1057.72,1429.94 1058.76,1430.03 1059.79,1430 1060.83,1430 1061.87,1429.95 1062.91,1430.04 1063.94,1430.12 1064.98,1430.23 1066.02,1430.18 \n",
       "  1067.06,1430.23 1068.09,1430.21 1069.13,1430.22 1070.17,1430.35 1071.21,1430.34 1072.25,1430.38 1073.28,1430.45 1074.32,1430.41 1075.36,1430.32 1076.4,1430.32 \n",
       "  1077.43,1430.14 1078.47,1430.26 1079.51,1430.21 1080.55,1430.22 1081.58,1430.21 1082.62,1430.18 1083.66,1430.21 1084.7,1430.13 1085.74,1430.28 1086.77,1430.33 \n",
       "  1087.81,1430.42 1088.85,1430.39 1089.89,1430.35 1090.92,1430.48 1091.96,1430.6 1093,1430.57 1094.04,1430.62 1095.08,1430.57 1096.11,1430.67 1097.15,1430.68 \n",
       "  1098.19,1430.73 1099.23,1430.75 1100.26,1430.79 1101.3,1430.86 1102.34,1430.86 1103.38,1430.68 1104.41,1430.74 1105.45,1430.69 1106.49,1430.68 1107.53,1430.7 \n",
       "  1108.57,1430.8 1109.6,1430.74 1110.64,1430.68 1111.68,1430.83 1112.72,1430.78 1113.75,1430.8 1114.79,1430.76 1115.83,1430.89 1116.87,1430.82 1117.91,1430.93 \n",
       "  1118.94,1430.94 1119.98,1431.02 1121.02,1431 1122.06,1431.05 1123.09,1431.08 1124.13,1431.1 1125.17,1431.11 1126.21,1431.06 1127.24,1431.09 1128.28,1431.14 \n",
       "  1129.32,1431.19 1130.36,1431.29 1131.4,1431.34 1132.43,1431.28 1133.47,1431.28 1134.51,1431.4 1135.55,1431.43 1136.58,1431.46 1137.62,1431.41 1138.66,1431.47 \n",
       "  1139.7,1431.46 1140.73,1431.44 1141.77,1431.51 1142.81,1431.53 1143.85,1431.6 1144.89,1431.62 1145.92,1431.69 1146.96,1431.82 1148,1431.9 1149.04,1431.92 \n",
       "  1150.07,1432.02 1151.11,1431.95 1152.15,1431.96 1153.19,1432.01 1154.23,1432.08 1155.26,1432.15 1156.3,1432.13 1157.34,1432.16 1158.38,1432.1 1159.41,1432.08 \n",
       "  1160.45,1432.07 1161.49,1432.09 1162.53,1432.01 1163.56,1432 1164.6,1432.16 1165.64,1432.17 1166.68,1432.18 1167.72,1432.25 1168.75,1432.19 1169.79,1432.29 \n",
       "  1170.83,1432.35 1171.87,1432.38 1172.9,1432.46 1173.94,1432.64 1174.98,1432.6 1176.02,1432.67 1177.05,1432.73 1178.09,1432.81 1179.13,1432.71 1180.17,1432.83 \n",
       "  1181.21,1432.81 1182.24,1432.75 1183.28,1432.69 1184.32,1432.82 1185.36,1432.85 1186.39,1432.86 1187.43,1432.75 1188.47,1432.85 1189.51,1432.87 1190.55,1432.95 \n",
       "  1191.58,1433.01 1192.62,1432.99 1193.66,1433.12 1194.7,1433.21 1195.73,1433.21 1196.77,1433.28 1197.81,1433.32 1198.85,1433.32 1199.88,1433.34 1200.92,1433.47 \n",
       "  1201.96,1433.53 1203,1433.64 1204.04,1433.59 1205.07,1433.66 1206.11,1433.76 1207.15,1433.79 1208.19,1433.81 1209.22,1433.85 1210.26,1433.84 1211.3,1433.92 \n",
       "  1212.34,1433.98 1213.37,1433.92 1214.41,1433.85 1215.45,1433.88 1216.49,1434.01 1217.53,1434.05 1218.56,1434.05 1219.6,1434.11 1220.64,1434.07 1221.68,1434.08 \n",
       "  1222.71,1434.2 1223.75,1434.18 1224.79,1434.13 1225.83,1434.2 1226.87,1434.21 1227.9,1434.25 1228.94,1434.28 1229.98,1434.34 1231.02,1434.36 1232.05,1434.36 \n",
       "  1233.09,1434.41 1234.13,1434.43 1235.17,1434.37 1236.2,1434.38 1237.24,1434.31 1238.28,1434.34 1239.32,1434.29 1240.36,1434.28 1241.39,1434.33 1242.43,1434.34 \n",
       "  1243.47,1434.35 1244.51,1434.44 1245.54,1434.47 1246.58,1434.58 1247.62,1434.72 1248.66,1434.69 1249.69,1434.72 1250.73,1434.76 1251.77,1434.78 1252.81,1434.8 \n",
       "  1253.85,1434.8 1254.88,1434.8 1255.92,1434.84 1256.96,1434.78 1258,1434.8 1259.03,1434.84 1260.07,1434.81 1261.11,1434.89 1262.15,1434.92 1263.19,1434.99 \n",
       "  1264.22,1435.05 1265.26,1435.13 1266.3,1435.06 1267.34,1435.08 1268.37,1435.11 1269.41,1435.15 1270.45,1435.25 1271.49,1435.25 1272.52,1435.28 1273.56,1435.28 \n",
       "  1274.6,1435.24 1275.64,1435.28 1276.68,1435.22 1277.71,1435.17 1278.75,1435.17 1279.79,1435.16 1280.83,1435.26 1281.86,1435.31 1282.9,1435.37 1283.94,1435.35 \n",
       "  1284.98,1435.41 1286.01,1435.5 1287.05,1435.62 1288.09,1435.66 1289.13,1435.73 1290.17,1435.75 1291.2,1435.76 1292.24,1435.83 1293.28,1435.82 1294.32,1435.76 \n",
       "  1295.35,1435.84 1296.39,1435.82 1297.43,1435.91 1298.47,1435.86 1299.51,1435.85 1300.54,1435.81 1301.58,1435.76 1302.62,1435.74 1303.66,1435.73 1304.69,1435.8 \n",
       "  1305.73,1435.87 1306.77,1435.84 1307.81,1435.92 1308.84,1435.94 1309.88,1436 1310.92,1436.02 1311.96,1436.02 1313,1436.04 1314.03,1436.12 1315.07,1436.13 \n",
       "  1316.11,1436.19 1317.15,1436.24 1318.18,1436.22 1319.22,1436.26 1320.26,1436.31 1321.3,1436.32 1322.34,1436.29 1323.37,1436.26 1324.41,1436.19 1325.45,1436.22 \n",
       "  1326.49,1436.22 1327.52,1436.22 1328.56,1436.2 1329.6,1436.19 1330.64,1436.18 1331.67,1436.11 1332.71,1436.1 1333.75,1436.16 1334.79,1436.25 1335.83,1436.25 \n",
       "  1336.86,1436.35 1337.9,1436.38 1338.94,1436.49 1339.98,1436.57 1341.01,1436.64 1342.05,1436.71 1343.09,1436.82 1344.13,1436.84 1345.16,1436.84 1346.2,1436.81 \n",
       "  1347.24,1436.82 1348.28,1436.82 1349.32,1436.78 1350.35,1436.86 1351.39,1436.87 1352.43,1436.98 1353.47,1437.06 1354.5,1437.06 1355.54,1437.08 1356.58,1437.1 \n",
       "  1357.62,1437.08 1358.66,1437.13 1359.69,1437.22 1360.73,1437.28 1361.77,1437.32 1362.81,1437.23 1363.84,1437.17 1364.88,1437.26 1365.92,1437.22 1366.96,1437.2 \n",
       "  1367.99,1437.25 1369.03,1437.23 1370.07,1437.27 1371.11,1437.29 1372.15,1437.26 1373.18,1437.34 1374.22,1437.32 1375.26,1437.3 1376.3,1437.34 1377.33,1437.43 \n",
       "  1378.37,1437.48 1379.41,1437.47 1380.45,1437.45 1381.48,1437.47 1382.52,1437.49 1383.56,1437.52 1384.6,1437.58 1385.64,1437.56 1386.67,1437.61 1387.71,1437.67 \n",
       "  1388.75,1437.76 1389.79,1437.8 1390.82,1437.74 1391.86,1437.76 1392.9,1437.8 1393.94,1437.86 1394.98,1437.78 1396.01,1437.7 1397.05,1437.67 1398.09,1437.68 \n",
       "  1399.13,1437.69 1400.16,1437.64 1401.2,1437.69 1402.24,1437.66 1403.28,1437.64 1404.31,1437.61 1405.35,1437.62 1406.39,1437.69 1407.43,1437.66 1408.47,1437.61 \n",
       "  1409.5,1437.69 1410.54,1437.67 1411.58,1437.71 1412.62,1437.78 1413.65,1437.71 1414.69,1437.66 1415.73,1437.68 1416.77,1437.71 1417.8,1437.74 1418.84,1437.77 \n",
       "  1419.88,1437.78 1420.92,1437.84 1421.96,1437.82 1422.99,1437.84 1424.03,1437.93 1425.07,1437.88 1426.11,1437.9 1427.14,1437.94 1428.18,1437.95 1429.22,1437.99 \n",
       "  1430.26,1438.02 1431.3,1437.99 1432.33,1437.99 1433.37,1437.93 1434.41,1437.98 1435.45,1438.1 1436.48,1438.19 1437.52,1438.29 1438.56,1438.22 1439.6,1438.24 \n",
       "  1440.63,1438.28 1441.67,1438.31 1442.71,1438.34 1443.75,1438.33 1444.79,1438.38 1445.82,1438.38 1446.86,1438.37 1447.9,1438.42 1448.94,1438.39 1449.97,1438.41 \n",
       "  1451.01,1438.52 1452.05,1438.53 1453.09,1438.58 1454.12,1438.57 1455.16,1438.58 1456.2,1438.54 1457.24,1438.6 1458.28,1438.62 1459.31,1438.65 1460.35,1438.58 \n",
       "  1461.39,1438.56 1462.43,1438.63 1463.46,1438.66 1464.5,1438.62 1465.54,1438.64 1466.58,1438.67 1467.62,1438.63 1468.65,1438.6 1469.69,1438.5 1470.73,1438.52 \n",
       "  1471.77,1438.55 1472.8,1438.58 1473.84,1438.55 1474.88,1438.54 1475.92,1438.57 1476.95,1438.53 1477.99,1438.52 1479.03,1438.55 1480.07,1438.61 1481.11,1438.64 \n",
       "  1482.14,1438.7 1483.18,1438.64 1484.22,1438.68 1485.26,1438.7 1486.29,1438.63 1487.33,1438.62 1488.37,1438.65 1489.41,1438.62 1490.45,1438.67 1491.48,1438.7 \n",
       "  1492.52,1438.75 1493.56,1438.78 1494.6,1438.7 1495.63,1438.74 1496.67,1438.7 1497.71,1438.63 1498.75,1438.66 1499.78,1438.69 1500.82,1438.72 1501.86,1438.7 \n",
       "  1502.9,1438.76 1503.94,1438.75 1504.97,1438.75 1506.01,1438.73 1507.05,1438.75 1508.09,1438.7 1509.12,1438.79 1510.16,1438.79 1511.2,1438.86 1512.24,1438.85 \n",
       "  1513.27,1438.87 1514.31,1438.85 1515.35,1438.89 1516.39,1438.92 1517.43,1438.86 1518.46,1438.9 1519.5,1438.9 1520.54,1438.94 1521.58,1438.97 1522.61,1439.04 \n",
       "  1523.65,1439.13 1524.69,1439.14 1525.73,1439.14 1526.77,1439.18 1527.8,1439.23 1528.84,1439.26 1529.88,1439.28 1530.92,1439.33 1531.95,1439.29 1532.99,1439.29 \n",
       "  1534.03,1439.3 1535.07,1439.26 1536.1,1439.21 1537.14,1439.19 1538.18,1439.17 1539.22,1439.17 1540.26,1439.2 1541.29,1439.15 1542.33,1439.17 1543.37,1439.12 \n",
       "  1544.41,1439.15 1545.44,1439.19 1546.48,1439.24 1547.52,1439.27 1548.56,1439.37 1549.59,1439.45 1550.63,1439.4 1551.67,1439.36 1552.71,1439.38 1553.75,1439.42 \n",
       "  1554.78,1439.44 1555.82,1439.51 1556.86,1439.44 1557.9,1439.37 1558.93,1439.36 1559.97,1439.38 1561.01,1439.41 1562.05,1439.5 1563.09,1439.46 1564.12,1439.45 \n",
       "  1565.16,1439.49 1566.2,1439.5 1567.24,1439.57 1568.27,1439.52 1569.31,1439.54 1570.35,1439.55 1571.39,1439.61 1572.42,1439.63 1573.46,1439.64 1574.5,1439.61 \n",
       "  1575.54,1439.62 1576.58,1439.56 1577.61,1439.54 1578.65,1439.57 1579.69,1439.55 1580.73,1439.63 1581.76,1439.64 1582.8,1439.69 1583.84,1439.69 1584.88,1439.67 \n",
       "  1585.91,1439.64 1586.95,1439.73 1587.99,1439.71 1589.03,1439.78 1590.07,1439.74 1591.1,1439.8 1592.14,1439.86 1593.18,1439.87 1594.22,1439.88 1595.25,1440 \n",
       "  1596.29,1440.03 1597.33,1440.11 1598.37,1440.08 1599.41,1440.13 1600.44,1440.05 1601.48,1440.08 1602.52,1440.09 1603.56,1440.1 1604.59,1440.14 1605.63,1440.16 \n",
       "  1606.67,1440.16 1607.71,1440.19 1608.74,1440.21 1609.78,1440.25 1610.82,1440.21 1611.86,1440.2 1612.9,1440.22 1613.93,1440.18 1614.97,1440.19 1616.01,1440.23 \n",
       "  1617.05,1440.3 1618.08,1440.29 1619.12,1440.3 1620.16,1440.37 1621.2,1440.35 1622.23,1440.42 1623.27,1440.46 1624.31,1440.52 1625.35,1440.49 1626.39,1440.56 \n",
       "  1627.42,1440.52 1628.46,1440.48 1629.5,1440.41 1630.54,1440.47 1631.57,1440.46 1632.61,1440.46 1633.65,1440.42 1634.69,1440.41 1635.73,1440.38 1636.76,1440.36 \n",
       "  1637.8,1440.4 1638.84,1440.33 1639.88,1440.41 1640.91,1440.43 1641.95,1440.49 1642.99,1440.51 1644.03,1440.5 1645.06,1440.52 1646.1,1440.47 1647.14,1440.51 \n",
       "  1648.18,1440.51 1649.22,1440.51 1650.25,1440.49 1651.29,1440.52 1652.33,1440.47 1653.37,1440.46 1654.4,1440.51 1655.44,1440.52 1656.48,1440.55 1657.52,1440.54 \n",
       "  1658.56,1440.55 1659.59,1440.56 1660.63,1440.55 1661.67,1440.6 1662.71,1440.63 1663.74,1440.67 1664.78,1440.71 1665.82,1440.71 1666.86,1440.73 1667.89,1440.87 \n",
       "  1668.93,1440.95 1669.97,1440.96 1671.01,1440.96 1672.05,1440.99 1673.08,1441.11 1674.12,1441.02 1675.16,1440.93 1676.2,1441 1677.23,1441.01 1678.27,1440.97 \n",
       "  1679.31,1441.01 1680.35,1440.97 1681.38,1441.02 1682.42,1441.01 1683.46,1441 1684.5,1441.01 1685.54,1441.07 1686.57,1441.15 1687.61,1441.13 1688.65,1441.11 \n",
       "  1689.69,1441.12 1690.72,1441.08 1691.76,1441.09 1692.8,1441.11 1693.84,1441.11 1694.88,1441.1 1695.91,1441.14 1696.95,1441.15 1697.99,1441.1 1699.03,1441.18 \n",
       "  1700.06,1441.16 1701.1,1441.17 1702.14,1441.14 1703.18,1441.12 1704.21,1441.16 1705.25,1441.14 1706.29,1441.12 1707.33,1441.14 1708.37,1441.13 1709.4,1441.13 \n",
       "  1710.44,1441.18 1711.48,1441.25 1712.52,1441.24 1713.55,1441.18 1714.59,1441.12 1715.63,1441.14 1716.67,1441.13 1717.7,1441.14 1718.74,1441.17 1719.78,1441.17 \n",
       "  1720.82,1441.26 1721.86,1441.25 1722.89,1441.24 1723.93,1441.25 1724.97,1441.23 1726.01,1441.28 1727.04,1441.27 1728.08,1441.27 1729.12,1441.3 1730.16,1441.33 \n",
       "  1731.2,1441.35 1732.23,1441.41 1733.27,1441.37 1734.31,1441.37 1735.35,1441.43 1736.38,1441.47 1737.42,1441.48 1738.46,1441.44 1739.5,1441.5 1740.53,1441.48 \n",
       "  1741.57,1441.48 1742.61,1441.52 1743.65,1441.51 1744.69,1441.58 1745.72,1441.57 1746.76,1441.58 1747.8,1441.64 1748.84,1441.62 1749.87,1441.67 1750.91,1441.73 \n",
       "  1751.95,1441.73 1752.99,1441.73 1754.02,1441.77 1755.06,1441.76 1756.1,1441.76 1757.14,1441.79 1758.18,1441.86 1759.21,1441.84 1760.25,1441.82 1761.29,1441.84 \n",
       "  1762.33,1441.95 1763.36,1441.9 1764.4,1441.89 1765.44,1441.85 1766.48,1441.85 1767.52,1441.82 1768.55,1441.82 1769.59,1441.8 1770.63,1441.82 1771.67,1441.85 \n",
       "  1772.7,1441.87 1773.74,1441.88 1774.78,1441.87 1775.82,1441.85 1776.85,1441.88 1777.89,1441.9 1778.93,1441.9 1779.97,1441.89 1781.01,1442.02 1782.04,1442.07 \n",
       "  1783.08,1442.06 1784.12,1442.12 1785.16,1442.18 1786.19,1442.19 1787.23,1442.21 1788.27,1442.22 1789.31,1442.24 1790.34,1442.25 1791.38,1442.32 1792.42,1442.4 \n",
       "  1793.46,1442.4 1794.5,1442.43 1795.53,1442.46 1796.57,1442.45 1797.61,1442.49 1798.65,1442.51 1799.68,1442.51 1800.72,1442.54 1801.76,1442.6 1802.8,1442.61 \n",
       "  1803.84,1442.61 1804.87,1442.68 1805.91,1442.66 1806.95,1442.72 1807.99,1442.76 1809.02,1442.76 1810.06,1442.74 1811.1,1442.72 1812.14,1442.69 1813.17,1442.76 \n",
       "  1814.21,1442.73 1815.25,1442.71 1816.29,1442.74 1817.33,1442.77 1818.36,1442.81 1819.4,1442.78 1820.44,1442.78 1821.48,1442.85 1822.51,1442.92 1823.55,1442.93 \n",
       "  1824.59,1442.92 1825.63,1442.94 1826.67,1442.97 1827.7,1442.95 1828.74,1442.99 1829.78,1442.97 1830.82,1442.92 1831.85,1442.92 1832.89,1442.94 1833.93,1442.97 \n",
       "  1834.97,1442.97 1836,1442.95 1837.04,1442.96 1838.08,1442.96 1839.12,1442.97 1840.16,1442.96 1841.19,1442.94 1842.23,1442.93 1843.27,1442.95 1844.31,1442.94 \n",
       "  1845.34,1442.86 1846.38,1442.83 1847.42,1442.82 1848.46,1442.88 1849.49,1442.9 1850.53,1442.93 1851.57,1442.91 1852.61,1442.91 1853.65,1442.89 1854.68,1442.89 \n",
       "  1855.72,1442.93 1856.76,1442.93 1857.8,1442.94 1858.83,1442.89 1859.87,1442.9 1860.91,1442.91 1861.95,1442.89 1862.99,1442.87 1864.02,1442.86 1865.06,1442.88 \n",
       "  1866.1,1442.9 1867.14,1442.89 1868.17,1442.89 1869.21,1442.88 1870.25,1442.86 1871.29,1442.86 1872.32,1442.83 1873.36,1442.82 1874.4,1442.85 1875.44,1442.85 \n",
       "  1876.48,1442.84 1877.51,1442.82 1878.55,1442.8 1879.59,1442.79 1880.63,1442.77 1881.66,1442.79 1882.7,1442.79 1883.74,1442.8 1884.78,1442.83 1885.81,1442.89 \n",
       "  1886.85,1442.88 1887.89,1442.94 1888.93,1442.99 1889.97,1443.03 1891,1443.13 1892.04,1443.18 1893.08,1443.2 1894.12,1443.21 1895.15,1443.18 1896.19,1443.21 \n",
       "  1897.23,1443.22 1898.27,1443.21 1899.31,1443.22 1900.34,1443.2 1901.38,1443.25 1902.42,1443.28 1903.46,1443.38 1904.49,1443.3 1905.53,1443.33 1906.57,1443.34 \n",
       "  1907.61,1443.33 1908.64,1443.33 1909.68,1443.34 1910.72,1443.28 1911.76,1443.32 1912.8,1443.31 1913.83,1443.32 1914.87,1443.3 1915.91,1443.32 1916.95,1443.33 \n",
       "  1917.98,1443.36 1919.02,1443.37 1920.06,1443.38 1921.1,1443.38 1922.13,1443.45 1923.17,1443.44 1924.21,1443.44 1925.25,1443.47 1926.29,1443.48 1927.32,1443.51 \n",
       "  1928.36,1443.51 1929.4,1443.49 1930.44,1443.45 1931.47,1443.44 1932.51,1443.38 1933.55,1443.39 1934.59,1443.39 1935.63,1443.35 1936.66,1443.38 1937.7,1443.48 \n",
       "  1938.74,1443.49 1939.78,1443.52 1940.81,1443.54 1941.85,1443.54 1942.89,1443.53 1943.93,1443.54 1944.96,1443.58 1946,1443.59 1947.04,1443.58 1948.08,1443.59 \n",
       "  1949.12,1443.64 1950.15,1443.68 1951.19,1443.73 1952.23,1443.76 1953.27,1443.74 1954.3,1443.78 1955.34,1443.8 1956.38,1443.8 1957.42,1443.75 1958.45,1443.77 \n",
       "  1959.49,1443.75 1960.53,1443.74 1961.57,1443.78 1962.61,1443.78 1963.64,1443.83 1964.68,1443.89 1965.72,1443.96 1966.76,1444.01 1967.79,1444.02 1968.83,1444.06 \n",
       "  1969.87,1444.04 1970.91,1444.04 1971.95,1444 1972.98,1443.96 1974.02,1443.95 1975.06,1444 1976.1,1444.03 1977.13,1444 1978.17,1443.94 1979.21,1443.93 \n",
       "  1980.25,1443.88 1981.28,1443.92 1982.32,1443.96 1983.36,1443.99 1984.4,1444.01 1985.44,1444.03 1986.47,1444 1987.51,1443.98 1988.55,1443.99 1989.59,1444.02 \n",
       "  1990.62,1444 1991.66,1443.99 1992.7,1443.99 1993.74,1444.02 1994.78,1444.03 1995.81,1444.06 1996.85,1444.09 1997.89,1444.11 1998.93,1444.15 1999.96,1444.16 \n",
       "  2001,1444.16 2002.04,1444.2 2003.08,1444.2 2004.11,1444.25 2005.15,1444.28 2006.19,1444.29 2007.23,1444.27 2008.27,1444.28 2009.3,1444.32 2010.34,1444.3 \n",
       "  2011.38,1444.33 2012.42,1444.33 2013.45,1444.37 2014.49,1444.36 2015.53,1444.36 2016.57,1444.37 2017.6,1444.38 2018.64,1444.36 2019.68,1444.37 2020.72,1444.39 \n",
       "  2021.76,1444.34 2022.79,1444.32 2023.83,1444.29 2024.87,1444.29 2025.91,1444.24 2026.94,1444.25 2027.98,1444.24 2029.02,1444.26 2030.06,1444.29 2031.1,1444.3 \n",
       "  2032.13,1444.41 2033.17,1444.38 2034.21,1444.4 2035.25,1444.34 2036.28,1444.34 2037.32,1444.36 2038.36,1444.35 2039.4,1444.4 2040.43,1444.37 2041.47,1444.37 \n",
       "  2042.51,1444.37 2043.55,1444.41 2044.59,1444.39 2045.62,1444.37 2046.66,1444.38 2047.7,1444.37 2048.74,1444.41 2049.77,1444.4 2050.81,1444.46 2051.85,1444.5 \n",
       "  2052.89,1444.48 2053.92,1444.47 2054.96,1444.52 2056,1444.59 2057.04,1444.6 2058.08,1444.58 2059.11,1444.56 2060.15,1444.55 2061.19,1444.59 2062.23,1444.57 \n",
       "  2063.26,1444.59 2064.3,1444.62 2065.34,1444.65 2066.38,1444.68 2067.42,1444.7 2068.45,1444.72 2069.49,1444.78 2070.53,1444.75 2071.57,1444.78 2072.6,1444.78 \n",
       "  2073.64,1444.79 2074.68,1444.84 2075.72,1444.82 2076.75,1444.85 2077.79,1444.88 2078.83,1444.88 2079.87,1444.89 2080.91,1444.85 2081.94,1444.9 2082.98,1444.95 \n",
       "  2084.02,1444.95 2085.06,1444.96 2086.09,1444.97 2087.13,1444.96 2088.17,1445.02 2089.21,1444.94 2090.24,1444.95 2091.28,1444.94 2092.32,1444.99 2093.36,1445.07 \n",
       "  2094.4,1445.11 2095.43,1445.13 2096.47,1445.07 2097.51,1445.05 2098.55,1445.08 2099.58,1445.07 2100.62,1445.06 2101.66,1445.07 2102.7,1445.09 2103.74,1445.08 \n",
       "  2104.77,1445.09 2105.81,1445.07 2106.85,1445.06 2107.89,1445.04 2108.92,1445.07 2109.96,1445.11 2111,1445.11 2112.04,1445.16 2113.07,1445.2 2114.11,1445.2 \n",
       "  2115.15,1445.25 2116.19,1445.27 2117.23,1445.24 2118.26,1445.24 2119.3,1445.18 2120.34,1445.18 2121.38,1445.22 2122.41,1445.22 2123.45,1445.23 2124.49,1445.3 \n",
       "  2125.53,1445.32 2126.56,1445.34 2127.6,1445.37 2128.64,1445.34 2129.68,1445.38 2130.72,1445.45 2131.75,1445.48 2132.79,1445.47 2133.83,1445.46 2134.87,1445.49 \n",
       "  2135.9,1445.49 2136.94,1445.51 2137.98,1445.56 2139.02,1445.56 2140.06,1445.54 2141.09,1445.56 2142.13,1445.61 2143.17,1445.63 2144.21,1445.6 2145.24,1445.58 \n",
       "  2146.28,1445.59 2147.32,1445.52 2148.36,1445.51 2149.39,1445.51 2150.43,1445.53 2151.47,1445.59 2152.51,1445.53 2153.55,1445.55 2154.58,1445.55 2155.62,1445.52 \n",
       "  2156.66,1445.55 2157.7,1445.54 2158.73,1445.55 2159.77,1445.58 2160.81,1445.55 2161.85,1445.55 2162.89,1445.51 2163.92,1445.54 2164.96,1445.58 2166,1445.53 \n",
       "  2167.04,1445.54 2168.07,1445.54 2169.11,1445.53 2170.15,1445.55 2171.19,1445.56 2172.22,1445.61 2173.26,1445.65 2174.3,1445.67 2175.34,1445.67 2176.38,1445.7 \n",
       "  2177.41,1445.75 2178.45,1445.78 2179.49,1445.78 2180.53,1445.76 2181.56,1445.77 2182.6,1445.81 2183.64,1445.79 2184.68,1445.83 2185.71,1445.82 2186.75,1445.81 \n",
       "  2187.79,1445.83 2188.83,1445.88 2189.87,1445.93 2190.9,1445.96 2191.94,1445.97 2192.98,1446 2194.02,1446.02 2195.05,1446.05 2196.09,1446.08 2197.13,1446.12 \n",
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      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function run_once(b)\n",
    "    rms = Float64[]\n",
    "    distribution = randn(b)\n",
    "    expectation = mean(distribution)\n",
    "    sample_avg = SampleAvg()\n",
    "    \n",
    "    for i in 1:2*b\n",
    "        avg = sample_avg(distribution[rand(1:b)])\n",
    "        push!(rms, abs(avg - expectation))\n",
    "    end\n",
    "    rms\n",
    "end\n",
    "\n",
    "n_runs = 1000\n",
    "p = plot(legend=:topright)\n",
    "\n",
    "for b in [2, 10, 100, 1000]\n",
    "    rms = mean(run_once(b) for _ in 1:n_runs)\n",
    "    xs = (1:2*b) ./ b\n",
    "    plot!(p, xs, rms, label=\"b=$b\")\n",
    "end\n",
    "\n",
    "p\n"
   ]
  }
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